Question: For real numbers $x$, let \[f(x) = \left\{
\begin{array}{cl}
x+2 &\text{ if }x>3, \\
2x+a &\text{ if }x\le 3.
\end{array}
\right.\]What must the value of $a$ be to make the piecewise function continuous (which means that its graph can be drawn without lifting your pencil from the paper)?
Answer: For the function to be continuous, both of the two expressions must have the same value when $x=3$. Therefore, $3+2=2(3)+a$. Solving, we get that $a=\boxed{-1}$.